Iran's top security body has ordered local journalists not to report on problems caused by petrol rationing, a day after its surprise introduction.
Iranian TV initially did not mention the unrest at petrol stations
Angry motorists have reacted violently to the curbs, attacking up to 19 petrol stations in the capital, Tehran.
There are still long queues outside filling stations.
The authorities switched off the mobile text messaging system in Tehran overnight to prevent motorists from organising more protests.
The BBC's Frances Harrison in Tehran said that many Iranians are already on edge because of a recent sharp rise in the cost of living.
During Wednesday's unrest, motorists threw stones and shouted slogans against President Mahmoud Ahmadinejad.
Despite the ban on negative reporting by Iran's security council, reformist papers are still complained about the abrupt way in which it was announced, saying even the police chief and the petrol station owners were not aware of the move.
Hardline papers have advised motorists not to use their personal cars too much and to share vehicles in order to save petrol.
Iranian TV initially did not mention the unrest and mostly interviewed people who said they supported the rationing.
Although the daily allowance is just over three litres, motorists can take their whole month's allowance of 100 litres in one go.
This has caused confusion with some drivers who wrongly believed that the rationing had not started yet and rushing to fill up their tanks, our correspondent says.
She says the government is trying to rein in fuel consumption over fears of possible UN sanctions over its nuclear programme.
Despite its huge energy reserves, Iran lacks refining capacity and it imports about 40% of its petrol.
The country has a large budget deficit largely caused by fuel subsidies and the inflation rate is estimated at 20-30%.